Soft and hard QCD dynamics in hadroproduction of charmonium

TL;DR

This paper develops a unified framework for charmonium hadroproduction by combining perturbative QCD (both NLO matrix elements and LO+PS Monte Carlo) with non-perturbative formation mechanisms, namely the Colour Evaporation Model (CEM) and the Soft Colour Interaction (SCI) model. It demonstrates that hard and soft QCD dynamics jointly shape total cross sections and differential distributions (xF and pT) for J/ψ and related states across fixed-target and Tevatron energies, and it introduces an improved cc̄~charmonium mapping that accounts for energy-dependent state ratios. The work shows NLO corrections greatly affect normalization and high-pT tails, but LO+PS can mimic these effects with an adjusted charm mass, while the SCI and CEM formalisms provide normalised, experimentally compatible soft dynamics. The improved mass-mapping scheme further aligns the predicted relative rates of J/ψ, ψ′, and χc, offering a more predictive description of non-perturbative charmonium formation. Overall, the study supports a coherent, multi-scale approach to charmonium production with practical Monte Carlo implementations for phenomenology and data interpretation.

Abstract

Both hard and soft QCD dynamics are important in charmonium production, as presented here through a next-to-leading order QCD matrix element calculation combined with the colour evaporation model. Observed $x_F$ and $p_\perp$ distributions of $J/ψ$ in hadroproduction at fixed target and $p\bar{p}$ collider energies are reproduced. Quite similar results can also be obtained in a more phenomenologically useful Monte Carlo event generator where the perturbative production of \ccbar pairs is instead obtained through leading order matrix elements and the parton shower approximation of the higher order processes. The soft dynamics may alternatively be described by the soft colour interaction model, originally introduced in connection with rapidity gaps. We also discuss the relative rates of different charmonium states and introduce an improved model for mapping the continuous \ccbar mass spectrum on the physical charmonium resonances.

Figures (11)

• Figure 1: Illustration of $c\bar{c}$ production processes in (a) leading order and (b) next-to-leading order perturbative QCD.
• Figure 2: Total cross section of $J/\psi$, $\psi^{\prime}$ and open charm ($D$ mesons) in proton-proton interactions at invariant mass $\sqrt s$; curves obtained from the CEM-NLO model (colour evaporation model combined with NLO pQCD matrix elements) in comparison to a compilation of data sigtotpsisigtotoppp800300.
• Figure 3: Distributions in $x_F$ and $p_\perp^2$ of $J/\psi$ produced with proton beams of energies $800$, $530$ and $300\, GeV$ on fixed target. Data pp800300pp800kpp530 compared to CEM based on NLO pQCD matrix elements, and CEM and SCI based on LO matrix elements plus parton showers in the Pythia Monte Carlo.
• Figure 4: Distributions in $x_F$ and $p_\perp^2$ of $J/\psi$ (in 800 GeV proton on proton as in Fig. \ref{['pp']}) from variations of the pQCD treatment. CEM based on the NLO program with $m_c=1.5$ GeV: NLO and LO matrix elements, NLO with no intrinsic $k_\perp$. CEM based on Pythia with $m_c=1.35$ GeV: LO matrix elements plus parton showers (PS) and PS contribution shown separately.
• Figure 5: Distributions in $x_F$ and $p_\perp^2$ of $J/\psi$ produced with antiproton beams of energies 300 and 125 GeV on fixed target. Data 300125 compared to CEM based on NLO pQCD matrix elements, and CEM and SCI based on LO matrix elements plus parton showers in the Pythia Monte Carlo.